Problems in the classical calculus of variations

This dissertation concerns convergence analysis for nonparametric problems in the calculus of variations and sufficient conditions for weak local minimizer of a functional for both nonparametric and parametric problems. Newton's method in infinite-dimensional space is proved to be well-defined and converges quadratically to a weak local minimizer of a functional subject to certain boundary conditions. Sufficient conditions for global converges are proposed and a well-defined algorithm based on those conditions is presented and proved to converge. Finite element discretization is employed to achieve an implementable line-search-based quasi-Newton algorithm and a proof of convergence of the discretization of the algorithm is included. This work also proposes sufficient conditions for weak local minimizer without using the language of conjugate points. The form of new conditions is consistent with the ones in finite-dimensional case. It is believed that the new form of sufficient conditions will lead to simpler approaches to verify an extremal as local minimizer for well-known problems in calculus of variations.

BUILDING A DISCOURSE: BRIDGING THE GAP BETWEEN NEW MEDIA'S CONVERGENCE AND RHETORIC AND COMPOSITION'S MULTIMODALITY

My dissertation emphasizes the use of narrative structuralism and narrative theories about storytelling in order to build a discourse between the fields of New Media and Rhetoric and Composition. Propp's morphological analysis and the breaking down of stories into component pieces aides in the discussion of storytelling as it appears in and is mediated by digital and computer technologies. New Media and Rhetoric and Composition are aided by shared concerns for textual production and consumption. In using the notion of "kairotic reading" (KR), I show the interconnectedness and interdisciplinarity required in the development of pedagogy utilized to teach students to develop into reflective practitioners that are aware of their rhetorical surroundings and can made sound judgments concerning their own message generation and consumption in the workplace. KR is a transferable skill that is beneficial to students and teachers alike. The dissertation research utilizes theories of New Media and New Media-influenced practitioners, including Jenkins' theory of convergence, Bourdieu's notion of taste, Gee's term "semiotic domains," and Manovich's "modification." These theoretical pieces are combined in order to show how KR can be extended by convergent narrative practices. In order to build connections with New Media, the consideration and inclusion of Kress and van Leeuwen's multimodality, Selber's "reflective practitioners," and Selfe's definition of multimodal composing allow for a greater establishment of conversation order to create a richer conversation around the implications of metacognitive development and practitioner reflexivity with scholars in New Media. My research also includes analysis of two popular media franchises Deborah Harkness' A Discovery of Witches and Fox's Bones television series to show similarities and differences among convergence-linked and multimodal narratives. Lastly, I also provide example assignments that can be taken, further developed, and utilized in classrooms engaging in multimodal composing practices. This dissertation pushes consideration of New Media into the work already being performed by those in Rhetoric and Composition.